write a word phrase for the expression 10 + (6 minus 4)?

Answer:

Y =8x +1

Step-by-step explanation:

Answer:

a) The correct option is C: 4x

b) The correct option is B: 2x

Step-by-step explanation:

a) Usually when we have a real number multiplying a variable, we do not need to write the multiplication symbol.

So instead of writing:

4×x

We can write:

4x

And this will be equivalent.

Then in this case the correct option is C.

b) We know that if we have the multiplication of A by n, this will be equivalent to add A n times.

Then if we have the sum of A, for example, 4 times, we have:

A + A + A + A

And this can be written as 4*A

In this case, we have the expression x + x.

So we are adding x two times, then this can be written as: 2*x, or, as we said earlier, this also can be written as 2x.

Then the correct option is option B.

Answer:

Current insurance cost = \(685.43\) $

Step-by-step explanation:

Given

Reduced Amount = \(4.1\%\:\times\:714.73\)

                              \(=\left(\frac{4.1}{100}\right)\left(714.73\right)\)

                              \(=\frac{41\times \:714.73}{1000}\)

                               \(=29.30\) $

Current Insurance cost = \(714.73 - 29.30\)

                                       = \(685.43\) $

Thus,

Current insurance cost = \(685.43\) $

The double integral ∬R (x^2 + y) dA over the annular region R is equal to zero.

To evaluate the double integral over the annular region R, we need to determine the limits of integration. The annular region is bounded by two circles: x^2 + y^2 = 1 and x^2 + y^2 = 5.

In polar coordinates, the equation of the inner circle is r = 1, and the equation of the outer circle is r = √5.

Since we are integrating over the entire region R, we can express the limits of integration as follows: θ varies from 0 to 2π, and r varies from 1 to √5.

The integrand is (x^2 + y), which can be written in polar coordinates as (r^2 * cos^2θ + r * sinθ).

When we integrate this expression over the annular region R, we find that the contribution from each infinitesimal area element cancels out, resulting in a total value of zero.

Therefore, the value of the double integral (x^2 + y) dA over the annular region R is zero.

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Answer:$7.49

Step-by-step explanation:

just subtract 42.50 from 49.99
49.99-42.50=7.49

The equations are

a) Julie can type 25 words in 1 minute and Debbie can type 20 words in 1 minute

b) Julie can type 1500 words in 1 hour and Debbie can type 1200 words in 1 hour

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of words typed by Julie be = J

Let the number of words typed by Debbie be = D

a)

Now ,

Julie can type 50 words in 2 minutes

So , the number of words Julie can type in 1 minute = 50 / 2

Number of words Julie can type in 1 minute = 25 words

And ,

Debbie can type 300 words in 15 minutes

So , the number of words Debbie can type in 1 minute = 300 / 15

Number of words Debbie can type in 1 minute = 20 words

b)

1 hour = 60 minutes

The number words Julie can type in 1 hour = Number of words Julie can type in 1 minute x 60

Substituting the values in the equation , we get

The number words Julie can type in 1 hour = 25 x 60

The number words Julie can type in 1 hour = 1500 words

And ,

The number words Debbie can type in 1 hour = Number of words Debbie can type in 1 minute x 60

Substituting the values in the equation , we get

The number words Debbie can type in 1 hour = 20 x 60

The number words Debbie can type in 1 hour = 1200 words

Hence , the number of words per hour for Julie and Debbie are 1500 and 1200 respectively

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There are 16 more stamps from France than Germany.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Scott's stamp collection:

Germany = 59

Spain = 53

France = 75

The difference between the number of stamps between Germany and France.

= 75 - 59

= 16

Thus,

There are 16 more stamps from France than Germany.

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We can say with 90% confidence that the true mean GPA of all accounting students at this university lies between 2.7107 and 3.0493.

We are given:

Sample size n = 21

Sample mean X = 2.88

Sample standard deviation s = 0.16

Confidence level = 90% or α = 0.10 (since α = 1 - confidence level)

Since the sample size is small and population standard deviation is unknown, we will use a t-distribution to construct the confidence interval.

The formula for the confidence interval is given by:

X ± t(α/2, n-1) * s/√n

where t(α/2, n-1) is the t-score with (n-1) degrees of freedom, corresponding to the upper α/2 percentage point of the t-distribution.

Using a t-table with (n-1) = 20 degrees of freedom and α/2 = 0.05, we find the t-score to be 1.725.

Plugging in the values, we get:

2.88 ± 1.725 * 0.16/√21

= (2.7107, 3.0493)

Therefore, we can say with 90% confidence that the true mean GPA of all accounting students at this university lies between 2.7107 and 3.0493.

Note: The confidence interval can also be written as [2.71, 3.05] rounding to two decimal places.

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Answer:

75 minutes

Step-by-step explanation:

To calculate the time it will take for Faisal to drive 100 km, we can use a proportion based on the given information:

\(\sf \dfrac{Time \; 1}{Distance\;1}=\dfrac{Time\;2}{Distance\;2}\)

Given:

Substitute these values into the proportion:

\(\sf \dfrac{30\;min}{40\;km}=\dfrac{Time\;2}{100\;km}\)

To find Time 2, we can multiply both sides by 100 km:

\(\sf \dfrac{30\;min}{40\;km}\times 100\;km=\dfrac{Time\;2}{100\;km} \times 100\;km\)

\(\sf Time \; 2 = \dfrac{30 \; minutes \times 100 \; km}{40\;km}\)

Solve for Time 2:

\(\sf Time \; 2 = \dfrac{30 \; minutes \times 100}{40}\)

\(\sf Time \; 2 = \dfrac{3000 \; minutes}{40}\)

\(\sf Time\;2=75\;minutes\)

Therefore, it will take Faisal 75 minutes to drive 100 km.

The formula for the entries of \(M^{n}\), where n is a positive integer is \(=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right]\)  for M = \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\) .

Let us find the formula for entries of \(M^{n}\), where n is a positive integer.

Let M be a 2 x 2 matrix  \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\)

we get the eigenvalues and their associated eigenvectors as follows-

Eigenvalue : 9λ , multiplicity : 1λ, eigenvector : [ 1, 1]

Eigenvalue : 7λ , multiplicity : 1λ, eigenvector : [ 0.5, 1]

now, we have

\({\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right] }\) = \(\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]^{-1}\) \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\)  \(\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]\)

              = \(\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right]\)  \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\)  \(\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]\)

hence, \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\) = \(\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]\)  \(\left[\begin{array}{cc}9 & 0 \\0 & 7\end{array}\right]\)  \(\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right]\)

So,

\({\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]^n } & =\left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right]^n\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right]\)

                    \(= \left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{cc}9^n & 0 \\0 & 7^n\end{array}\right]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right]\)

                    \(=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right]\)

Thus, the formula for the entries of \(M^{n}\), where n is a positive integer is \(=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right]\) for M = \(\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]\) .

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Answer:

B. Selling treasury securities

Step-by-step explanation:

I'm taking the quiz

The Federal Reserve can reduce the amount of money available in the economy is buying treasury securities.

Therefore, the correct answer exists as option B. Selling treasury securities.

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The researcher needs a sample of at least 46 days.

We have,

To estimate the true mean water temperature within 4 with 90% confidence, given that the variance is 27%, we need to use the formula for sample size in a confidence interval estimation:
n = (Z² x σ²) / E²
where n is the required sample size, Z is the Z-score corresponding to the desired confidence level (90%), σ^2 is the variance (27%), and E is the margin of error (4).

We can find the Z-score for a 90% confidence level using a standard normal table, which is 1.645.
Now we can plug the values into the formula:
n = (1.645² x 0.27) / 4²
n = (2.706025 x 0.27) / 16
n = 0.729625 / 16
n = 0.0456015625

Since we cannot have a fraction of a day, we need to round up to the nearest whole number to ensure the desired accuracy.

Therefore, the researcher needs a sample of at least 46 days to estimate the true mean water temperature within 4 with 90% confidence.

Thus,

The researcher needs a sample of at least 46 days.

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Answer:

12

Step-by-step explanation:

3(4)=12

The 4th term of the sequence is 12.

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.

In the sequence 1, 3, 5, 7, 9, …, 1 is the first term, 3 is the second term, 5 is the third term, and so on.

Given:

sequence, S(n): 3n

Now, to find the 4th term of sequence we have to put n= 4.

So, the term of sequence

S(4) = 3(4)

s(4) = 12

Hence, the 4th term is 12.

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Answer:

The answer is x = 9

We use Pythagoras theorem to form the equation and solve for x

That's

a² = b² + c²

where a is the hypotenuse

we get

(x + 6)² = 12² + x²

Expand

x² + 12x + 36 = 144 + x²

Group like terms

We have

x² - x ² + 12x = 144 - 36

12x = 108

Divide both sides by 9

That's

12x/12 = 108/12

x = 9

Hope this helps you.

Answer:

Solution,

AB=(perpendicular)=X

AC(hypotenuse)=X+6

CB(Base)=13

Using Pythagoras theorem,

\( {h}^{2} = {p}^{2} + {b}^{2} \\ {(x + 6)}^{2} = {x}^{2} + {(12)}^{2} \\ {x}^{2} + 12x + 36 = {x}^{2} + 144 \\ 12x + 36 = 144 \\ 12x = 144 - 36 \\ 12x = 108 \\ x = \frac{108}{12} \\ x = 9\)

Hope this helps...

Good luck on your assignment...

Answer: B

The answer above is correct. It would be 5pi/3.

Step-by-step explanation: Edge2021

I just got it right on my quiz.

The value of the x is equal to the 5pi/3.

The expression is

\(\sin \left(11\cdot \frac{\pi }{2}+x\right)=-\frac{1}{2},\:\pi \le \:x\le \:2\pi\)

The value of the given expression.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

We have,

\(\sin \left(11\cdot \frac{\pi }{2}+x\right)=-\frac{1}{2},\:\pi \le \:x\le \:2\pi\)

\(11\cdot \frac{\pi }{2}+x=\frac{7\pi }{6}+2\pi n,\:11\cdot \frac{\pi }{2}+x=\frac{11\pi }{6}+2\pi n\)

\(x=2\pi n-\frac{13\pi }{3},\:x=2\pi n-\frac{11\pi }{3}\)

\(x=\frac{5\pi }{3}\)

Therefore, The value of the x is equal to the 5pi/3.

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Given any real number x, the ceiling of x, denoted as ⌈x⌉, is the smallest integer n such that n is greater than or equal to x.

In other words, ⌈x⌉ is the unique integer n that satisfies the following two conditions:

n is greater than or equal to x

n is the smallest integer that satisfies condition 1

For example, if x = 2.4, then ⌈x⌉ = 3 because 3 is the smallest integer that is greater than or equal to 2.4. Similarly, if x = -1.9, then ⌈x⌉ = -1 because -1 is the smallest integer that is greater than or equal to -1.9.

The ceiling function is useful in various mathematical and computational contexts, such as in rounding up numbers, calculating the smallest integer greater than or equal to a given value, and approximating functions.

It is a fundamental concept in discrete mathematics and is used in many applications, including computer science, optimization, and operations research.

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The values of f(1/2) and f(1/4) , rounded to the nearest hundredth, are 1.73 and 1.32

To find the values of f(1/2) and f(1/4) for the function y = f(x) = \(3^x\), we simply substitute the given values of x into the function and evaluate:

f(1/2) =\(3^(1/2)\)≈ 1.73

f(1/4) =\(3^(1/4)\)≈ 1.32

Rounded to the nearest hundredth, f(1/2) is approximately 1.73, and f(1/4) is approximately 1.32.

To understand how these values were obtained, it's helpful to recall that 3^x represents the exponential function with base 3, where x is the exponent. When x is a fraction, the function gives the value of the exponential power of the base 3 that corresponds to that fraction.

For example, when x = 1/2, the function evaluates to 3^(1/2), which is the square root of 3. This value is approximately 1.73 when rounded to the nearest hundredth.

Similarly, when x = 1/4, the function evaluates to 3^(1/4), which is the fourth root of 3. This value is approximately 1.32 when rounded to the nearest hundredth.

Similarly, when x = 1/4, the function evaluates to 3^(1/4), which is the fourth root of 3. This value is approximately 1.32 when rounded to the nearest hundredth.

Therefore, f(1/2) is approximately 1.73, and f(1/4) is approximately 1.32, rounded to the nearest hundredth.

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The vertical motion model is h(t) = -16t² + 54t + 3The equation above is in the standard form of a quadratic equation which is given as y = ax² + bx + c.The maximum point of a parabola (quadratic equation) is always at the vertex of the parabola. The formula for finding the x-coordinate of the vertex is given by -b/2a.

Using the above formula to find the time taken to reach the maximum height, we can find the time by finding the x-coordinate of the vertex of the quadratic equation, t = -b/2a.Substitute a = -16, b = 54 into the formula:$$\begin{aligned} t &= \frac{-b}{2a}\\ &= \frac{-54}{2(-16)}\\ &= 1.69 \end{aligned}$$Therefore, the time taken to reach the maximum height is 1.69 seconds (rounded to the nearest tenth).To find the maximum height reached by the object, we need to substitute t = 1.69 into the equation and solve for h(t):$$\begin{aligned} h(t) &= -16t^2 + 54t + 3\\ &= -16(1.69)^2 + 54(1.69) + 3\\ &= 49.13 \end{aligned}$$

Therefore, the maximum height reached by the object is 49.1 feet (rounded to the nearest tenth).Maximum height reached by an object = 49.1 feetTime taken to reach the maximum height = 1.69 seconds

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The equations of the asymptotes of the given hyperbola are; y = ±(40/9)x

We are given;

Vertex at (0,−40)

Focus at (0, 41).

Thus, the equation of the asymptote of the given hyperbola is;

y = ±(40/(√41 - (-40))

y = ±(40/(√81)

y = ±40/9

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The area of the shaded region in this problem is given as follows:

995.44 cm².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, hence it's measure is given as follows:

r = 21 cm.

Then the area of the entire circle is given as follows:

A = π x 21²

A = 1385.44 cm².

The right triangle has two sides of length 39 cm and 20 cm, hence it's area is given as follows:

A = 0.5 x 39 x 10

A = 390 cm².

Then the area of the shaded region is given as follows:

1385.44 - 390 = 995.44 cm².

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If you choose the rebate offer, your monthly payment for the car loan at the bank will be approximately $557 (rounded to the nearest dollar).

To calculate the monthly payment for each financing option, we'll use the information provided:

1. 0% financing for 48 months:

Since the financing is offered at 0% interest, the monthly payment can be calculated by dividing the total purchase price by the number of months.

Purchase Price: $26,050

Number of Months: 48

Monthly Payment = Purchase Price / Number of Months

Monthly Payment = $26,050 / 48 ≈ $543

Therefore, the monthly payment for the 0% financing option for 48 months is approximately $543.

2. Rebate offer and car loan at the bank:

If you choose the rebate offer, you'll need to finance the remaining balance after deducting the rebate amount. Let's calculate the remaining balance:

Purchase Price: $26,050

Rebate Offer: $2,900

Remaining Balance = Purchase Price - Rebate Offer

Remaining Balance = $26,050 - $2,900 = $23,150

Now, we'll calculate the monthly payment using the remaining balance and the loan terms from the local bank:

Remaining Balance: $23,150

Interest Rate: 5.24% (compounded monthly)

Number of Months: 48

Monthly Payment = (Remaining Balance * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

First, let's calculate the Monthly Interest Rate:

Monthly Interest Rate = Annual Interest Rate / 12

Monthly Interest Rate = 5.24% / 12 ≈ 0.437%

Now, we can calculate the Monthly Payment using the formula mentioned above:

Monthly Payment = ($23,150 * 0.437%) / (1 - (1 + 0.437%)^(-48))

Monthly Payment ≈ $557

Therefore, if you choose the rebate offer, your monthly payment for the car loan at the bank will be approximately $557 (rounded to the nearest dollar).

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Answer:

B        

Step-by-step explanation:

Since point A and B are negative, we have to find the Absolute Value

And since we're trying to find the distance between them we need to subtract

Answer:

25.1

Step-by-step explanation:

for perimeter you just add them all together

Answer:

Her sales after 6 months are = 127units

Step-by-step explanation:

Percentage increase:- The degree to which a value increases expressed in percent form is known as percentage increase.

formula for % increase = (final value - initial value)/initial value(100)

Here in the question,

percentage increase after every month is = 5%

initial value  =  95 units

therefore by applying above formula :-

[(x-95)/95]×100 = 5          [where x is the value of her sales goals after 1 month]

x = (5/100)×95+ 95

x = 99.75

Now this x will be the initial value for the next month

x₂ = (5/100)99.75+ 99.75             [ x₂ = sales goal after 2 months]

x₂ = (5/100)×99.75+ 99.75

x₂ = 104.73

similarly,

(x₃-104.73/104.73)100 = 5       [x₃ = sales after 3 months]

x₃ = 109.96

similarly for 4th month,

(x₄ -109.96/109.96)100 = 5       [x₄ = sales after 4 months]

x₄ = 115.45

for 5th month,

(x₅ -115.45/115.45)100 = 5       [x₅ = sales after 5 months]

x₅ = 121.22

finally for the 6th month

(x₆-121.22/121.22)100 = 5        [x₆ = sales after 6 months]

x₆ = 127.28

therefore,

her sales after 6 months are = 127.28 units or 127 units by rounding off

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21) You most likely mean the number 0.666…. If x = 0.666…, then

10x = 6.666…

10x - x = 6.666… - 0.666…

9x = 6

x = 6/2 = 2/3

22) You either mean 1.2555… (only 5 repeats) or 1.252525… (both 2 and 5 repeat).

If x = 1.2555…, then

10x = 12.555…

100x = 125.555…

100x - 10x = 125.555… - 12.555…

90x = 113

x = 113/90

Otherwise, if x = 1.252525…, then

100x = 125.252525…

100x - x = 125.252525… - 1.252525…

99x = 124

x = 124/99

23) You either mean 0.4555… or 0.454545….

If x = 0.4555…, then

10x = 4.555…

100x = 45.555…

100x - 10x = 45.555… - 4.555…

90x = 41

x = 41/90

Otherwise, if x = 0.454545…, then

100x = 45.454545…

100x - x = 45.454545… - 0.454545…

99x = 45

x = 45/99 = 5/11

To express the given system of differential equation as an almost linear system, we need to find the partial derivatives of the given functions with respect to x and y.

∂f/∂x = -ex
∂f/∂y = 2
∂g/∂x = -1
∂g/∂y = -4cosy

Now, substituting these values in the general form of an almost linear system,

x′(t) = ax + by + r(x,y)
y′(t) = cx + dy + s(x,y)

we get,

x′(t) = -ex + 2y
y′(t) = -x - 4cosy

So,

a = -e, b = 2, c = -1, d = 0

At the critical point (0,0), the Jacobian matrix is

J(0,0) = ⎡⎣⎢⎢⎢-1 2⎤⎦⎥⎥⎥

The eigenvalues of this matrix can be found by solving the characteristic equation,

det(J - λI) = 0

where I is the identity matrix of the same size as J.

det ⎡⎣⎢⎢⎢-1-λ 2⎤⎦⎥⎥⎥ = (-1-λ)(-λ) - 2(2) = λ^2 + λ - 4

Using the quadratic formula, we get the eigenvalues as

λ1 = (-1 + sqrt(17))/2 ≈ 0.56
λ2 = (-1 - sqrt(17))/2 ≈ -2.56

Since the eigenvalues have opposite signs, the critical point is a saddle.

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The solution to the equation 2x + 9 = 15 is x = 3.

In the given linear equation, 2x + 9 = 15, we are tasked with finding the value of x that satisfies the equation. To solve it, we need to isolate the variable x on one side of the equation.

To begin, we subtract 9 from both sides of the equation, which gives us 2x = 15 - 9. Simplifying further, we have 2x = 6.

Next, to solve for x, we divide both sides of the equation by 2. This yields x = 6/2, which simplifies to x = 3.

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The value of the surface integral is `8(5√5 - 2√2 - 1)/15`.

The surface integral can be evaluated by first calculating the surface area element `dS` of the cone with given parametric equations. `dS` is obtained by finding the cross product of the partial derivatives of `x(u,v), y(u,v)`, and `z(u,v)` with respect to `u` and `v`.

Then, the surface integral can be calculated by integrating the product of `xyz` and `dS` over the surface `S`. Here's how to evaluate the surface integral:

Given that `S` is the cone with parametric equations `x=ucos(v), y=usin(v), z=u`, `0≤u≤2`, `0≤v≤2π`.

The surface area element `dS` of the cone is given by: `dS = |r_u × r_v| du dv`where `r(u, v) = `.

Then, the partial derivatives of `r(u, v)` with respect to `u` and `v` are:`r_u = ` and `r_v = <-u sin(v), u cos(v), 0>`

Thus, the surface area element `dS` can be calculated as:

dS = |r_u × r_v| du dv= |<-u cos(v), -u sin(v), u>| du dv= u √(1+u²) du dv

Therefore, the surface integral ∬S xyz dS can be evaluated as follows:

`∬S xyz dS`=`∬(xyz) (u√(1+u²)) du dv` `(` using dS above `)``

= ∫(0 to 2π) [ ∫(0 to 2) [ ∫(0 to u) (u cos(v) * u sin(v) * u) u √(1+u²) du ] dv ]`

=` ∫(0 to 2π) [ ∫(0 to 2) [ u^5/5 * cos(v) * sin(v) * √(1+u²)/2 ] dv ] du`

(using the formula `∫cosθsinθdθ = (sin²θ)/2`)`

= ∫(0 to 2π) [ ∫(0 to 2) [ u^5/10 * sin(2v) * √(1+u²) ] dv ] du`

(simplifying further using `sin(2v) = 2sin(v)cos(v)`)

=` 8 ∫(0 to 2) [ u^5/10 √(1+u²) ] du`=` 8/15 [ (1+u²)^(5/2) - 1 ]

[from 0 to 2]`=` 8/15 [ (5√5 - 2√2) - 1 ]`

=` 8/15 (5√5 - 2√2 - 1)`

=` 8(5√5 - 2√2 - 1)/15`

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Answer: You multiply the probability of each "event" -- the selection of the desired number, by the probabilities of the other events.

Step-by-step explanation:

The probability of getting 1 as the first number is 1/5 (possibilities are 1,2,3,4,5)

The probability of getting 2 as the second number is 1/4 (possibilities are 2,3,4,5. 1 is gone)

The probability of getting 3 as the third number is 1/3 (possibilities are 3,4,5. 1 and 2 are gone)

So you multiply 1/5 × 1/4 × 1/3

Answer:

3.25

Step-by-step explanation:

total 18.25 - 2.00 tip = 16.25

16.25/5=3.25